JEE Main · 2005 · 08 May 2005 · Offline · Gravitation

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A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take

G = 6.67 \times 1 0^{- 11} Nm^{2} / kg^{2}

)

(A) $13.34 \times 1 0^{- 10} J$
(B) $3.33 \times 1 0^{- 10} J$
(C) $6.67 \times 1 0^{- 9} J$
(D) $6.67 \times 1 0^{- 10} J$ ✓ Correct

Answer: (D)

Solution

The work to carry the particle off to infinity equals the rise in gravitational potential energy,

W = 0 - (- \frac{GM m}{R}) = \frac{GM m}{R}

. With

M = 100

kg,

m = 0.01

kg and

R = 0.1

W = \frac{6.67 \times 1 0 ^{- 11} \times 100 \times 0.01}{0.1} = 6.67 \times 1 0^{- 10}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option

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